Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
14.2-a1
14.2-a
$1$
$1$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
14.2
\( 2 \cdot 7 \)
\( 2^{13} \cdot 7^{2} \)
$2.34466$
$(-23a+156), (-4a-27)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$5.794569323$
0.854362636
\( -\frac{3621929}{6272} a - \frac{4226507}{1568} \)
\( \bigl[1\) , \( a\) , \( 1\) , \( -4 a + 43\) , \( 3 a - 8\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-4a+43\right){x}+3a-8$
14.2-b1
14.2-b
$1$
$1$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
14.2
\( 2 \cdot 7 \)
\( 2^{13} \cdot 7^{2} \)
$2.34466$
$(-23a+156), (-4a-27)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.371815243$
$14.07641912$
1.543371442
\( -\frac{3621929}{6272} a - \frac{4226507}{1568} \)
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -19885747 a - 134871681\) , \( 141136021646 a + 957231071290\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-19885747a-134871681\right){x}+141136021646a+957231071290$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.